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====== Angular Coulomb Potentials ======
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The angular coulomb potentials are a combination of the regular coulomb potentials and a angular dependent term similar to MEAM:

$$
V=V_{Coulomb}+\frac{1}{2}\sum f_{ij}(r_{ij})f_{ik}(r_{ik})g_i(\cos(\theta_{ijk}))
$$

===== Number of potential functions =====

To describe a system of $N$ atom types you need $N(N+2)$ potentials.

^ # atom types ^ $\phi_{ij}$ ^ $f_{ij}$ ^ $g_i$ ^ Total # potentials ^
^ $N$ ^ $N(N+1)/2$ ^ $N(N+1)/2$ ^ $N$ ^ $N(N+2)$ ^
| 1 | 1 | 1 | 1 | 3 |
| 2 | 3 | 3 | 2 | 8 |
| 3 | 6 | 6 | 3 | 15 |
| 4 | 10 | 10 | 4 | 24 |

=====  Order of potential functions  =====

The potential table is assumed to be symmetric, i.e. the potential for the atom types 1-0 is the same as the potential 0-1.

The order of the potentials in the potential file for $N$ atom types is:

$\phi_{00}, \ldots, \phi_{0N}, \phi_{11}, \ldots, \phi_{1N}, \ldots, \phi_{NN}$\\
$f_{00}, \ldots, f_{0N}, f_{11}, \ldots, f_{1N}, \ldots, f_{NN}$\\
$g_0, \ldots, g_N$